Beamforming in MIMO systems

ABSTRACT

A beamforming method comprises transmitting a training sequence from a transmitter array employing a set of beamforming vectors from a beamforming codebook. A receive array employs a combining codebook to acquire channel state information from the received transmissions, and estimates a preferred beamforming vector and a preferred combining vector. At least the preferred beamforming vector (and, optionally, the preferred combining vector) is transmitted back to the transmitter array.

BACKGROUND OF THE INVENTION

I. Field of the Invention

This invention relates generally to wireless communication systems andmore particularly to beamforming in a millimeter-wave wirelesscommunication system.

II. Description of the Related Art

In one aspect of the related art, a dual-mode ultra-wideband (UWB)Physical Layer supporting single carrier and OFDM modulation employs acommon mode. The UWB Physical Layer may be used for millimeter wave(e.g., 60 GHz) communications. The common mode is a single-carrier modeused by both single-carrier and OFDM devices for beaconing,network-control signaling, and base-rate data communications. The commonmode is typically necessary for interoperability between differentdevices and different networks.

Millimeter-wave communications may also employ MIMO (multiple inputmultiple output) beamforming to provide both spatial diversity and arraygains. Conventional beamforming, such as Eigen-beamforming, requireschannel state information matrices or beamforming matrices to bereturned to the transmitting array. The IEEE 802.11n MAC/PHYSpecifications D0.04, March 2006, specifies feedback information thatincludes row and column sizes of the feedback matrices, subcarriergrouping size (or cluster size), quantization bit size, and an array ofactual quantized data elements starting in the order of the lowestsubcarrier index to the highest subcarrier index. For beamforming thatemploys precoding matrices, the feedback information can be reduced byreplacing beamforming matrix contents with indices of a precoding-matrixcodebook, such as described in the IEEE 802.16e MAC/PHY SpecificationsD12, 2005, and in D. J. Love, R. W. Heath Jr., and T. Strohmer,“Grassmannian Beamforming for Multiple-Input Multiple-Output WirelessSystems”, IEEE Trans. Information Theory, Vol. 49, No. 10, October 2003,pp. 2735-2747).

SUMMARY OF THE INVENTION

Embodiments disclosed herein are advantageous for systems employing UWBsignals. However, the invention is not intended to be limited to suchsystems, as other wireless systems may benefit from similar advantages.

In one embodiment of the invention, a piconet controller employs a frameformat for signaling to one or more wireless subscriber devices. Thepiconet controller and each of the one or more subscriber devices employantenna arrays. The piconet controller transmits a signal with a frameformat comprising a plurality of transmission segments, wherein each ofthe plurality of transmission segments is transmitted with a differentbeam pattern from a predetermined beamforming codebook.

The frame format also provides for a listening period that allows thepiconet controller to listen for feedback (e.g., an acknowledgment) fromthe one or more subscriber devices. The piconet controller receivespreferred beamforming weights calculated by each subscriber device andemploys the beamforming weights in its array for communicating with theone or more subscriber devices. The piconet controller may also receiveeach subscriber device's calculated combining weights.

In one embodiment of the invention, the piconet controller may performproactive beamforming in which it employs the beacon portion of asuperframe when the piconet controller is the data source for one ormore subscriber devices. In another embodiment, the piconet controllermay perform on-demand beamforming, which employs a Channel TimeAllocation (CTA) part of the superframe. On-demand beamforming istypically performed between two devices (e.g., between the piconetcontroller and a subscriber device, or between two subscriber devices).

The beacon portion includes a quasi-omni section and a directionalsection. The quasi-omni section may comprise a plurality of identicalquasi-omni (Q-omni) sub-beacons (S-beacons), also referred to astransmission segments, covering different (and possibly overlapping)geographical areas around the piconet controller. Each Q-omni S-beaconis transmitted using a different Q-omni beamforming pattern selectedfrom a Q-omni codebook. One Q-omni beamforming vector is used per Q-omnisub-beacon transmission.

The listening period also comprises a plurality of receiving segments.For example, the Contention Access Period (CAP) may be divided into aplurality of sub-CAPs. During the l^(th) sub-CAP, the piconet controlleris in receiving mode, and it employs the same Q-omni beamformer vectorused for transmission during the l^(th) Q-Omni beacon. The quasi-omnitransmissions convey information about the structure of the directionaltraining sections, and the directional training sections enable channelstate information (CSI) acquisition and tracking. The directionalsection comprises a plurality of repetitions of a training sequence(which may also be referred to as transmission segments), where eachrepetition is transmitted by the piconet controller with a differentorthogonal or quasi-orthogonal beamforming vector from an orthogonal (orquasi-orthogonal) codebook.

The applicant recognizes that the frame formats and methods describedwith respect to the piconet controller communicating with one or moresubscriber devices may also be employed by subscriber devicescommunicating with the piconet controller and/or other subscriberdevices.

In another embodiment of the invention, a subscriber device in a piconetis configured for selecting beamforming and combining weights. Thesubscriber device and the piconet controller both comprise an antennaarray. The subscriber device receives a signal comprising a plurality oftransmission segments transmitted by the piconet controller. Each of theplurality of transmission segments is transmitted with a different beampattern from a predetermined beamforming codebook. The subscriber devicereceives at least a subset of the plurality of transmission segments andestimates a preferred beamforming vector therefrom. The subscriberdevice also estimates a preferred combining vector for processing itreceives. At least the preferred beamforming vector is sent back to thepiconet controller during a listening period

The applicant recognizes that the frame formats and methods describedwith respect to the subscriber device communicating with the piconetcontroller may also be employed by the piconet controller communicatingwith one or more subscriber devices.

In a further embodiment of the invention, a quasi-omni acquisitionsignaling protocol comprises a first transceiver transmitting a number Lof quasi-omni packets followed by L listening periods (ACKs) until itreceives an ACK in one of the L listening periods (e.g., at the l^(th)listening period). The first transceiver selects the l^(th) Q-omnidirection for transmission from the Q-omni codebook. The secondtransceiver records its best Q-omni receiving direction and uses it forany future Q-omni reception.

Embodiments of the invention may also provide for a frame format fordirectional training employing periodic transmissions from the firsttransceiver to the second transceiver. For example, one cycle ofdirectional training sequences transmitted by the first transceiver maycorrespond to all J orthogonal (quasi-orthogonal) beamforming vectorsfrom a subset of the selected codebook. Each cycle is followed by alistening period (ACK) to listen to any feedback from the secondtransceiver.

The first transceiver repeats the period until the second transceiveracquires the CSI, H_(1→2)(n) for n=0, 1, . . . , N−1, or finds anadequate LQI. The second transceiver estimates w₁ and c₂ and couples atleast the w₁ estimate to the first transceiver during the listening(ACK) period. The first transceiver employs the w₁ beamforming estimateand the second transceiver employs the c₂ combining estimate fordownlink (1→2) data communications. These estimates may be updatedduring a subsequent tracking step. Furthermore, this procedure may beperformed for uplink (e.g., 2→1 data communications).

Embodiments of the invention may be optimized for minimum processingcomplexity, such as to enable suitability for real-time applications,rapid updates, low power consumption, and/or low cost processingcomponents. Particular embodiments of the invention may be configured toprovide for the previously recited features and advantages and/oralternative features and advantages.

Although particular embodiments are described herein, many variationsand permutations of these embodiments fall within the scope and spiritof the invention. Although some benefits and advantages of the preferredembodiments are mentioned, the scope of the invention is not intended tobe limited to particular benefits, uses, or objectives. Rather,embodiments of the invention are intended to be broadly applicable todifferent wireless technologies, system configurations, networks, andtransmission protocols, some of which are illustrated by way of examplein the figures and in the following description of the preferredembodiments. The detailed description and drawings are merelyillustrative of the invention rather than limiting, the scope of theinvention being defined by the appended claims and equivalents thereof.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments according to the present invention are understood withreference to the following figures.

FIG. 1 is a block diagram of an Asymmetric Antenna System, which may beemployed in accordance with embodiments of the invention.

FIG. 2A illustrates a beamforming method between a first transceiver anda second transceiver in accordance with an embodiment of the invention.

FIG. 2B illustrates a beamforming-tracking method in accordance with anembodiment of the invention.

FIG. 3A shows a pair of orthogonal antenna array patterns for atwo-element array with an element spacing of λ/2 and binarybeamforming/combining weights.

FIG. 3B shows antenna array patterns for a three-element linear arrayhaving an element spacing of λ/2 and binary beamforming/combiningweights.

FIG. 3C shows a four orthogonal beam patterns generated by afour-element linear array with an element spacing of λ/2 and binarybeamforming/combining weights.

FIG. 3D shows five orthogonal beam patterns of a five-element lineararray.

FIG. 3E shows beam patterns of a six-element linear array with λ/2element spacing.

FIG. 3F shows orthogonal beam patterns of a seven-element linear arraywith λ/2-spacing.

FIG. 3G shows the eight orthogonal beam patterns of an eight-elementlinear array with λ/2-spacing.

FIG. 4A shows four antenna array patterns for a two-element array withan element spacing of λ/2 and quadrature beamforming/combining weights.

FIG. 4B shows four antenna array patterns for a three-element arrayemploying an element spacing of λ/2 and quadrature beamforming/combiningweights.

FIG. 4C shows four orthogonal antenna array patterns for a four-elementarray employing an element spacing of λ/2 and quadraturebeamforming/combining weights.

FIG. 4D shows beam patterns corresponding to an alternative codebook fora four-element array employing quadrature weights and an element spacingof λ/2.

FIG. 4E shows beam patterns corresponding to an extended codebook for afour-element array.

FIG. 4F shows six antenna array patterns for a five-element arrayemploying an element spacing of λ/2 and quadrature beamforming/combiningweights.

FIG. 4G shows eight antenna array patterns may be produced by afive-element array employing an element spacing of λ/2 and quadraturebeamforming/combining weights.

FIG. 4H shows six non-orthogonal antenna array patterns for asix-element array employing an element spacing of λ/2 and quadraturebeamforming/combining weights.

FIG. 4I shows eight antenna array patterns for a six-element arrayemploying an element spacing of λ/2 and quadrature beamforming/combiningweights.

FIG. 4J shows eight antenna array patterns for a seven-element arrayemploying an element spacing of λ/2 and quadrature beamforming/combiningweights.

FIG. 4K shows eight orthogonal antenna array patterns for aneight-element array employing an element spacing of λ/2 and quadraturebeamforming/combining weights.

FIG. 4L shows twelve antenna array patterns for an eight-element arrayemploying an element spacing of λ/2 and quadrature beamforming/combiningweights.

FIG. 4M shows sixteen antenna array patterns for an eight-element arrayemploying an element spacing of λ/2 and quadrature beamforming/combiningweights.

FIG. 5A shows two complementary Golay patterns for a two-element arraycomprises two orthogonal beamforming (or combining) vectors

FIG. 5B shows three quasi-orthogonal beam patterns for a three-elementantenna array.

FIG. 5C shows a pair of Golay complementary patterns for a four-elementarray

FIG. 5D shows three quasi-orthogonal beam patterns corresponding to acodebook for a five-element array comprising three quasi-orthogonalbeam-forming vectors.

FIG. 5E shows three quasi-orthogonal beam patterns corresponding to acode book for a six-element array.

FIG. 5F shows three quasi-orthogonal beam patterns corresponding to acode book for a seven-element array.

FIG. 5G shows a pair of beam patterns generated from two complementaryGolay vectors for an eight-element array

FIG. 6A shows a pair of quasi-omni beam patterns for a two-elementarray.

FIG. 6B shows a pair of quasi-omni beam patterns of a three-elementarray employing quadrature weights.

FIG. 6C is a plot of two Golay complementary patterns generated by afour-element array with quadrature weights.

FIG. 6D shows a quasi-omni pattern with maximum directivity of 2.55 dBgenerated by a five-element array

FIGS. 7A-7D show quasi-omni beam patterns for a six-element arraycorresponding to vectors of a quasi-omni codebook

FIG. 8A shows a pair of Golay complementary patterns generated by asix-element array.

FIG. 8B shows three quasi-omni beam patterns generated by aseven-element array with quadrature weighting vectors.

FIG. 8C shows a pair of complementary beam patterns generated by aneight-element array with quadrature weighting vectors.

FIGS. 8D-8E show beam patterns with a pair of orthogonal beamforming/combining vectors generated for an eight element array.

FIG. 9 shows a superframe that may be employed in accordance withembodiments of the invention.

FIG. 10A shows the packet structure of an S-beacon for OFDM.

FIG. 10B shows the packet structure of an S-beacon for Single Carrier(SC) signaling.

FIG. 11A illustrates a short OFDM training sequence.

FIG. 11B shows a long OFDM training sequence.

FIG. 11C shows a short single-carrier training sequence.

FIG. 11D shows a long single carrier training sequence.

FIG. 12A shows a superframe comprising a plurality M of cycles.

FIG. 12B shows a cycle comprising a plurality of M superframes.

FIG. 13A shows a beamforming information element of a transmissionframe.

FIG. 13B shows an antenna array information portion of the beamforminginformation element.

FIG. 13C shows a training sequence information portion of thebeamforming information element.

FIG. 14A shows a superframe that may be employed in embodiments of theinvention.

FIG. 14B illustrates a quasi-omni acquisition signaling protocol inaccordance with an embodiment of the invention.

FIG. 15 illustrates a frame format for directional training employingperiodic transmissions from the first transceiver to the secondtransceiver.

FIG. 16A illustrates a method for performing proactive beamforming inaccordance with one embodiment of the invention.

FIG. 16B illustrates a method for performing on-demand beamforming inaccordance with an embodiment of the invention.

FIG. 17A is a flow diagram of an on-demand beamforming method for SAS inaccordance with one embodiment of the invention.

FIG. 17B illustrates steps of an on-demand beamforming method for AAS inaccordance with an embodiment of the invention.

FIG. 18A illustrates a method in accordance with an embodiment of theinvention that employs the frame format shown in FIG. 15.

FIG. 18B illustrates a method in accordance with an alternativeembodiment of the invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Accordingly, while the embodiments of the present disclosure aresusceptible to various modifications and alternative forms, specificexemplary embodiments thereof are shown by way of example in thedrawings and will herein be described in detail. It should beunderstood, however, that there is no intent to limit the invention tothe particular forms disclosed, but on the contrary, the invention is tocover all modifications, equivalents, and alternatives falling withinthe spirit and scope of the invention. Like numbers may refer to likeelements throughout the description of the figures.

It should also be noted that in some alternative implementations, thefunctions/acts noted in the blocks may occur out of the order noted inthe flowcharts. For example, two blocks shown in succession may in factbe executed substantially concurrently or the blocks may sometimes beexecuted in the reverse order, depending upon the functionality andprocedures involved.

A transceiver that employs the same antenna(s) for both transmission andreception is referred to as a Symmetric Antenna System (SAS). Atransceiver that employs one set of antennas for transmission andanother set of antennas for reception (such as shown in FIG. 1) isreferred to as an Asymmetric Antenna System (AAS). A first transceiver101 employs M_(T) transmit antennas and M_(R) receive antennas. A secondtransceiver 102 employs N_(T) transmit antennas and N_(R) receiveantennas.

Channel model H_(1→2) is used to express the propagation environmentwhen transceiver 101 transmits signals to transceiver 102. Similarly,channel model H_(2→1) expresses the propagation environment whentransceiver 102 transmits signals received by transceiver 101. Thechannel models may be used to express any of the possible antennaconfigurations that may be employed in the related art. Furthermore, thechannel models may be used to express different transmission protocols.In one embodiment of the invention, OFDM signaling with a cyclic prefixand an FFT length of N subcarriers may employ the same channel model asa transmission that is Single Carrier (SC) with a cyclic prefix having aburst length N. In such cases, it is typical to assume that the cyclicprefix is longer than any multipath delay spread between anytransmit-receive pair of antenna elements.

An OFDM symbol stream or SC burst x(t) generated at the firsttransceiver 101 is expressed by

${{x(t)} = {\sum\limits_{k = 0}^{N - 1}\;{s_{k}{\delta\left( {t - {kT}_{c}} \right)}}}},$where T_(c) is the sample (or chip) duration, and s_(k) represents thecomplex data. The symbol stream is modulated by a beamforming vectorw₁=[w_(1,1), w_(1,2), . . . , w_(1,M) _(T) ]^(T) prior to beingtransmitted into a communication channel. A MIMO channel may beexpressed by frequency domain Channel State Information (CSI):H_(1→2)(n)εC^(M) ^(T) ^(×N) ^(R)at frequency bin number n, such as

${{H_{1->2}(n)} = \begin{bmatrix}{h_{1,1}^{1->2}(n)} & {h_{1,2}^{1->2}(n)} & \ldots & {h_{1,N_{R}}^{1->2}(n)} \\{h_{2,1}^{1->2}(n)} & {h_{2,2}^{1->2}(n)} & \ldots & {h_{2,N_{R}}^{1->2}(n)} \\\vdots & \vdots & \ddots & \vdots \\{h_{M_{T},1}^{1->2}(n)} & {h_{M_{T},2}^{1->2}(n)} & \ldots & {h_{M_{T},N_{R}}^{1->2}(n)}\end{bmatrix}},$where the terms h_(i,j)(n) include both transmit and receive filtering,along with the channel response between the first transceiver's j^(th)transmit antenna and the second transceiver's i^(th) receive antenna.

Signals received at the second transceiver are processed with acombining vector c₂=[c_(2,1) c_(2,2) . . . c_(2,N) _(R) ]^(T) to producea combined baseband signal,y(t)=c ₂ ^(H) [Σs _(k)δ(t−kT _(c))

H _(1→2)(t)w ₁ +b(t)],where b(t) is the additive white Gaussian noise vector across thereceive antennas of the second transceiver.

The discrete channel model between the first transceiver's transmitterand the second transceiver's receiver is expressed by a Single InputSingle Output (SISO) channel,

$y_{r} = {{{c_{2}^{H}{\sum\limits_{k = 0}^{L - 1}\;{H_{k}s_{r - k}w_{1}}}} + {c_{2}b_{i}}} = {{\sum\limits_{k = 0}^{L - 1}\;{p_{k}s_{r - k}}} + b_{i}^{\prime}}}$where p_(k)=c₂ ^(H)H_(k)w₁, and i denotes the sample (or chip) indexwithin an OFDM sample (or single-carrier burst). The SISO channel has afrequency response at frequency bins n=0, 1, . . . , N−1 given byP _(n) =c ₂ ^(H) H _(1→2)(n)w ₁.The discrete-frequency received signal model is:Y _(n) =P _(n) S _(n) +B _(n),where [S₀, S₁, . . . , S_(N)] is the OFDM data symbol (or the FFT of theSC data burst), and [B₀, B₁, . . . , B_(N)] is the additive whiteGaussian noise vector.

The channel model expressing the channel between the secondtransceiver's transmitter to first transceiver's receiver is given byQ _(n) =c ₂ ^(H) H _(2→1)(n)w ₂For frequency bins n=0, 1, . . . , N−1. For both OFDM and SC, the Signalto Noise Ratio (SNR) on the n^(th) subcarrier is given by

$\begin{matrix}{{{SNR}_{n}^{1->2} = {\frac{E_{s}{P_{n}}^{2}}{N_{0}} = \frac{E_{s}{{c_{2}^{H}{H_{1->2}(n)}w_{1}}}^{2}}{N_{0}}}},} \\{{SNR}_{n}^{2->1} = {\frac{E_{s}{Q_{n}}^{2}}{N_{0}} = \frac{E_{s}{{c_{1}^{H}{H_{2->1}(n)}w_{2}}}^{2}}{N_{0}}}}\end{matrix}$

An effective SNR (ESNR) is defined as a mapping from the instantaneoussubcarriers SNRs to an equivalent SNR that takes into account ForwardError Correction (FEC). There are many methods that can be used tocompute the ESNR, including (by way of example, but without limitation)calculating the mean of the SNRs over the different subcarriers;employing a Quasi-Static Method (such as is commonly used in 3GPP2 and1xEV-DV/DO communication systems); employing a Capacity effective SINRmapping (CESM), which is also used in 3GPP2 and 1xEV-DV/DO communicationsystems; using a CESM technique based on Convex Metric (which may beemployed in 3GPP2 and 1xEV-DV/DO); and using an Exponential EffectiveSINR Mapping (EESM), which is also used in 3GPP2.

Different ESNR calculation methods may be used for SC and OFDM. Forexample, a Minimum Mean Square Error (MMSE) SC equalizer typically hasan ESNR that can be approximated by the average of the SNRs over thedifferent subcarriers. However, OFDM tends to have an ESNR that may bebest approximated using the geometric mean of the SNRs over thedifferent subcarriers. The various ESNR-calculation methods may befurther configured to account for additional parameters, such as FEC,receiver imperfections, and/or bit-error rate (BER).

Embodiments of the invention may provide for one or more beamformingalgorithms configured to select the beamforming vectors (w₁ and w₂) andthe combining vectors (c₁ and c₂) that maximize at least onesignal-quality parameter, such as the ESNR. In the general AAS case, thefirst transceiver 101 may transmit known information to the secondtransceiver 102, which then derives matrices characterizing the channelstate information. This enables estimates of w₁ and c₂ to be calculated.The second transceiver 102 may transmit known information to the firsttransceiver 101 to provide channel state information that allows forestimates of w₂ and c₁ to be calculated. Some embodiments of theinvention may employ known data symbols, pilot signals, or othertraining information to be transmitted for acquiring channel stateinformation. Alternative embodiments may employ blind adaptiveprocessing or other techniques utilizing unknown transmitted data toderive channel state information.

In AAS, both directions of the link are used to estimate the vectors w₁,w₂, c₂, and c₁. For SAS, the beamforming vectors w₁ and w₂ and thecombining vectors c₂ and c₁ in a particular direction should be equal.Thus, w₁=w₂ and c₂=c₁, and only one direction of the link may beemployed for calculating the vectors w₁, w₂, c₂, and c₁.

FIG. 2A illustrates a beamforming method between a first transceiver anda second transceiver in accordance with an embodiment of the invention.For example, one transceiver may be a piconet controller and the othertransceiver may be a piconet subscriber device. A channel stateinformation (CSI) acquisition step 201 enables the second transceiver toacquire a first CSI matrix, which is used to estimate the firsttransceiver's optimal (or preferred) beamforming vector w₁ and thesecond transceiver's optimal (or preferred) combining vector c₂. The CSIacquisition step may comprise configuring the first transceiver totransmit a subset of a beamforming codebook 211. Furthermore, the secondtransceiver may be configured to employ a subset of a combining codebook212 to acquire the first CSI matrix.

An estimation step 202 comprises producing the optimal beamformingvector w₁ and the optimal combining vector c₂. It should be appreciatedthat the terms optimal beamforming vector and optimal combining vectordenote estimates of optimal values, and the optimality of such estimatesmay be limited with respect to one or more processing constraints,including (but not limited to) loss of information due to quantization,simplifying assumptions that sacrifice some accuracy and/or precision inorder to reduce computational complexity, and limited processing time,which may limit the number of iterative calculations. Other constraintsmay apply. For example, in some embodiments, a beamforming and/orcombining vector resulting in a signal-quality metric above apredetermined threshold may be deemed as optimal relative to a subset ofavailable vectors. Accordingly, the term “preferred beamforming vector”is equivalent to optimal beamforming vector, as used herein. Similarly,the term “preferred combining vector” is equivalent to optimalbeamforming vector. The estimation 202 may employ any of variousoptimality criteria, such as EESM or mean SNR.

A feedback step 203 provides for sending the optimal beamforming vectorw₁ (and, optionally, the optimal combining vector c₂) to the firsttransceiver 101. For an AAS system, steps 201 to 203 are repeatedwherein the designations of “first transceiver” and “second transceiver”are swapped. Thus, an optimal beamforming vector w₂ and an optimalcombining vector c₁ are estimated.

FIG. 2B illustrates a beamforming-tracking method in accordance with anembodiment of the invention. A tracking step 204 provides for trackingthe beamforming and combining vectors. The tracking step 204 is similarto the acquisition step, except that the first transceiver transmits asubset of the beamforming codebook at a rate that is lower than the rateemployed during acquisition 201. Similarly, lower-rate updates 205 aremade to the optimal beamforming vector w₁ and the optimal combiningvector c₂, and the values w₁ and c₂ are fed back 206 to the firsttransceiver 201. For an AAS system, steps 204 to 206 are repeated,wherein the designations of “first transceiver” and “second transceiver”are swapped. Thus, the estimates for the optimal beamforming vector w₂and the optimal combining vector c₁ are updated.

For a uniformly spaced linear antenna array with N elements, the arrayfactor is defined by

${{A(\theta)} = {\sum\limits_{n = 1}^{N}{w_{n}{\mathbb{e}}^{{j2\pi}\;{n{({d/\lambda})}}\cos\;\theta}}}},$where d is the spacing between array elements, θ denotes the angle fromthe axis of the linear array, λ is wavelength, and w₁ is the arrayelement weight of the n^(th) array element. The antenna arraydirectivity is given by

${D = {{\frac{\max{{A(\theta)}}^{2}}{w^{H}{Kw}}\mspace{14mu}{where}\mspace{14mu} K_{n,m}} = {\frac{\sin\left\lbrack {2{\pi\left( {d/\lambda} \right)}\left( {n - m} \right)} \right\rbrack}{2{\pi\left( {d/\lambda} \right)}\left( {n - m} \right)}\mspace{14mu} n}}},{m = {{0\text{:}N} - 1}}$The maximum possible directivity is D_(Max)=N.

The array factor of a two-dimensional array is given by

${{A\left( {\theta,\varphi} \right)} = {\sum\limits_{m = 1}^{N_{x}}{\sum\limits_{n = 1}^{N_{y}}{w_{m,n}{\mathbb{e}}^{{j2\pi}{\lbrack{{{m{({d_{x}/\lambda})}}\sin\;{\theta cos}\;\varphi} + {{n{({d_{y}/\lambda})}}\sin\;{\theta sin}\;\varphi}}\rbrack}}}}}},$where d_(x) denotes array spacing along the x-axis, d_(y) is the arrayspacing along the y-axis, N_(x) is the number of elements along thex-axis, N_(y) is the number of elements along the y-axis, and φ is therotation angle from the x-axis. The antenna weights w_(mn) may beexpressed as w_(mn)=w_(x,m)w_(y,n), where m=0:N_(x)−1, and n=0:N_(y)−1.Thus, an antenna weight matrix may be expressed by W_(xy)=w_(x)w_(y)^(T).

The array factor of a two-dimensional array that is separable intoone-dimensional (x-axis and y-axis) array components is expressed as

A(θ, φ) = A_(x)(θ, φ)A_(y)(θ, φ)${A_{x}\left( {\theta,\varphi} \right)} = {\sum\limits_{n = 1}^{N_{x}}{w_{x,n}{\mathbb{e}}^{{j2\pi}\;{n{({d_{x}/\lambda})}}\sin\;{\theta cos}\;\varphi}}}$${A_{y}\left( {\theta,\varphi} \right)} = {\sum\limits_{n = 1}^{N_{y}}{w_{y,n}{\mathbb{e}}^{{j2\pi}\;{n{({d_{y}/\lambda})}}\sin\;{\theta sin}\;\varphi}}}$A 2-dimensional codebook W_(xy)εC^(N) ^(x) ^(×N) ^(y) is expressed usinga codebook for one-dimensional antenna arrays along the x-axis,w_(x)εC^(N) ^(x) ^(×1), and a codebook for one-dimensional arrays alongthe y-axis, w_(y)εC^(N) ^(y) ^(×1).

In one embodiment of the invention, antenna array weights may comprise0° or 180° for each antenna element. This is referred to as a binaryembodiment wherein the beamforming and/or combining weights are selectedfrom {+1, −1}. Thus, each antenna element is configured to transmit orreceive I+Q (phase 0°) or −(I+Q) (phase 180°) signals.

FIG. 3A shows a pair of orthogonal antenna array patterns for atwo-element array with an element spacing of λ/2 and binarybeamforming/combining weights. The codebook for this case comprises thepair of orthogonal beamforming/combining vectors given by the columns ofthe following weight matrix W

$W = {\begin{bmatrix}{+ 1} & {+ 1} \\{- 1} & {+ 1}\end{bmatrix}.}$The first beam pattern has its maximum at 0°, and the second beampattern is maximum at 90°.

FIG. 3B shows antenna array patterns for a three-element linear arrayhaving an element spacing of λ/2 and binary beamforming/combiningweights. The codebook comprises three beamforming/combining vectorsgiven by the columns of the weight matrix

$W = {\begin{bmatrix}{+ 1} & {+ 1} & {+ 1} \\{- 1} & {+ 1} & {+ 1} \\{+ 1} & {- 1} & {+ 1}\end{bmatrix}.}$In this case, the first beam pattern has its maximum at 0°, the secondbeam pattern is maximum at 60° and 120°, and the third pattern ismaximum at 90°.

In FIG. 3C, a four-element linear array with an element spacing of λ/2and binary beamforming/combining weights produces four orthogonal beampatterns. These beam patterns are characterized by a codebook of vectorsgiven by columns of the following weight matrix

$W = {\begin{bmatrix}{+ 1} & {+ 1} & {+ 1} & {+ 1} \\{- 1} & {- 1} & {+ 1} & {+ 1} \\{+ 1} & {- 1} & {- 1} & {+ 1} \\{- 1} & {+ 1} & {- 1} & {+ 1}\end{bmatrix}.}$

FIG. 3D shows five orthogonal beam patterns of a five-element lineararray corresponding to orthogonal codebook vectors given by columns ofthe weight matrix

$W = {\begin{bmatrix}{+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} \\{- 1} & {- 1} & {- 1} & {+ 1} & {+ 1} \\{+ 1} & {+ 1} & {- 1} & {- 1} & {+ 1} \\{- 1} & {+ 1} & {+ 1} & {- 1} & {+ 1} \\{+ 1} & {- 1} & {+ 1} & {- 1} & {+ 1}\end{bmatrix}.}$

FIG. 3E shows beam patterns of a six-element linear array with λ/2element spacing. Orthogonal codebook vectors are given by columns of thefollowing weight matrix

$W = {\begin{bmatrix}{+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} \\{- 1} & {- 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} \\{+ 1} & {- 1} & {- 1} & {- 1} & {+ 1} & {+ 1} \\{- 1} & {+ 1} & {+ 1} & {- 1} & {- 1} & {+ 1} \\{+ 1} & {- 1} & {+ 1} & {+ 1} & {- 1} & {+ 1} \\{- 1} & {+ 1} & {- 1} & {+ 1} & {- 1} & {+ 1}\end{bmatrix}.}$In an alternative embodiment, the following weight matrix may beemployed

$W = {\begin{bmatrix}{+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} \\{- 1} & {- 1} & {- 1} & {+ 1} & {+ 1} & {+ 1} \\{+ 1} & {+ 1} & {- 1} & {- 1} & {+ 1} & {+ 1} \\{- 1} & {+ 1} & {+ 1} & {- 1} & {- 1} & {+ 1} \\{+ 1} & {- 1} & {+ 1} & {+ 1} & {- 1} & {+ 1} \\{- 1} & {+ 1} & {- 1} & {+ 1} & {- 1} & {+ 1}\end{bmatrix}.}$

FIG. 3F shows orthogonal beam patterns of a seven-element linear arraywith λ/2-spacing. The beam patterns correspond to codebook vectors givenby columns of the weight matrix

$W = \begin{bmatrix}{+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} \\{- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {+ 1} & {+ 1} \\{+ 1} & {+ 1} & {- 1} & {- 1} & {- 1} & {- 1} & {+ 1} \\{- 1} & {+ 1} & {+ 1} & {+ 1} & {- 1} & {- 1} & {+ 1} \\{+ 1} & {- 1} & {- 1} & {+ 1} & {+ 1} & {- 1} & {+ 1} \\{- 1} & {+ 1} & {- 1} & {- 1} & {+ 1} & {- 1} & {+ 1} \\{+ 1} & {- 1} & {+ 1} & {- 1} & {+ 1} & {- 1} & {+ 1}\end{bmatrix}$

FIG. 3G shows the eight orthogonal beam patterns of an eight-elementlinear array with λ/2-spacing. The beam patterns correspond to codebookvectors given by columns of the following weight matrix

$W = {\begin{bmatrix}{+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} \\{- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {+ 1} & {+ 1} & {+ 1} \\{+ 1} & {+ 1} & {- 1} & {- 1} & {- 1} & {- 1} & {+ 1} & {+ 1} \\{- 1} & {- 1} & {+ 1} & {+ 1} & {- 1} & {- 1} & {+ 1} & {+ 1} \\{+ 1} & {- 1} & {- 1} & {+ 1} & {+ 1} & {- 1} & {- 1} & {+ 1} \\{- 1} & {+ 1} & {- 1} & {- 1} & {+ 1} & {- 1} & {- 1} & {+ 1} \\{+ 1} & {- 1} & {+ 1} & {- 1} & {- 1} & {+ 1} & {- 1} & {+ 1} \\{- 1} & {+ 1} & {- 1} & {+ 1} & {- 1} & {+ 1} & {- 1} & {+ 1}\end{bmatrix}.}$

In some embodiments of the invention, antenna array weights may comprisephases from the set of 0°, 90°, 180°, and 270°. Thus, quadrature weightsare selected from {+1, −1, +j, −j}. An embodiment of the invention mayprovide for transmitting and/or receiving signals characterized by I(0°), −I (180°), Q (270°), and −Q (90°). An equivalent set of signalscomprises I+Q, I−Q, −I+Q, and −I−Q.

FIG. 4A shows four antenna array patterns for a two-element array withan element spacing of λ/2 and quadrature beamforming/combining weights.The codebook for this case comprises the set of vectors given by thecolumns of the following weight matrix W

$W = {\begin{bmatrix}{+ 1} & {+ 1} & {+ 1} & {+ 1} \\{- 1} & {- j} & {+ 1} & {+ j}\end{bmatrix}.}$In this case, WW^(H)=4I.

FIG. 4B shows four antenna array patterns for a three-element arrayemploying an element spacing of λ/2 and quadrature beamforming/combiningweights. The codebook comprises the set of vectors given by the columnsof the following weight matrix

$W = {\begin{bmatrix}{+ 1} & {+ 1} & {+ 1} & {+ 1} \\{- 1} & {- j} & {+ 1} & {+ j} \\{+ 1} & {- 1} & {+ 1} & {- 1}\end{bmatrix}.}$In this case, WW^(H)=4I as well.

FIG. 4C shows four orthogonal antenna array patterns for a four-elementarray employing an element spacing of λ/2 and quadraturebeamforming/combining weights. The codebook comprises the set of fourorthogonal vectors given by the columns of the following weight matrix

$W = {\begin{bmatrix}{+ 1} & {+ 1} & {+ 1} & {+ 1} \\{- 1} & {- j} & {+ 1} & {+ j} \\{+ 1} & {- 1} & {+ 1} & {- 1} \\{- 1} & {+ j} & {+ 1} & {- j}\end{bmatrix}.}$

FIG. 4D shows beam patterns corresponding to an alternative codebook fora four-element array employing quadrature weights and an element spacingof λ/2. Six beam-forming/combining vectors are given by columns of theweight matrix

$W = {\left\lbrack {\begin{matrix}{+ 1} \\{- 1} \\{+ 1} \\{- 1}\end{matrix}\begin{matrix}{+ 1} \\{- j} \\{- 1} \\{+ 1}\end{matrix}\begin{matrix}{+ 1} & {+ 1} & {+ 1} & {+ 1} \\{+ 1} & {+ 1} & {+ j} & {- 1} \\{- j} & {+ 1} & {- 1} & {- j} \\{- 1} & {+ 1} & {- 1} & {+ 1}\end{matrix}} \right\rbrack.}$

Beam patterns corresponding to an extended codebook for a four-elementarray are shown in FIG. 4E. The array comprises elements with λ/2-spacedand quadrature beamforming/combining weights. The codebook comprises theset of eight vectors given by the columns of the following weight matrix

$W = {\begin{bmatrix}{+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} \\{- 1} & {- j} & {- j} & {- j} & {+ 1} & {+ j} & {+ j} & {+ j} \\{+ 1} & {+ j} & {- 1} & {- j} & {+ 1} & {+ j} & {- 1} & {- j} \\{- 1} & {+ 1} & {+ j} & {- 1} & {+ 1} & {- 1} & {- j} & {+ 1}\end{bmatrix}.}$

FIG. 4F shows six antenna array patterns for a five-element arrayemploying an element spacing of λ/2 and quadrature beamforming/combiningweights. The codebook comprises the set of vectors given by the columnsof the following weight matrix

$W = {\begin{bmatrix}{+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} \\{- 1} & {- j} & {- j} & {+ 1} & {+ j} & {+ j} \\{+ 1} & {+ j} & {- j} & {+ 1} & {- 1} & {- 1} \\{- 1} & {+ 1} & {- 1} & {+ 1} & {- 1} & {+ 1} \\{+ 1} & {- j} & {+ j} & {+ 1} & {- j} & {+ j}\end{bmatrix}.}$

In FIG. 4G, eight antenna array patterns may be produced by afive-element array employing an element spacing of λ/2 and quadraturebeamforming/combining weights according to a codebook of vectorsrepresented by columns of the following weight matrix

$W = {\begin{bmatrix}{+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} \\{- 1} & {- j} & {- j} & {- j} & {+ 1} & {+ j} & {+ j} & {+ j} \\{+ 1} & {+ j} & {- 1} & {- j} & {+ 1} & {+ j} & {- 1} & {- j} \\{- 1} & {+ 1} & {+ j} & {- 1} & {+ 1} & {- 1} & {- j} & {+ 1} \\{+ 1} & {- 1} & {+ 1} & {- 1} & {+ 1} & {- 1} & {+ 1} & {- 1}\end{bmatrix}.}$

FIG. 4H shows six non-orthogonal antenna array patterns for asix-element array employing an element spacing of λ/2 and quadraturebeamforming/combining weights. The codebook comprises the set of sixvectors given by the columns of the following weight matrix

$W = {\begin{bmatrix}{+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} \\{- 1} & {- j} & {- j} & {+ 1} & {+ j} & {+ j} \\{+ 1} & {+ j} & {- j} & {+ 1} & {+ j} & {- j} \\{- 1} & {+ 1} & {- 1} & {+ 1} & {- 1} & {+ 1} \\{+ 1} & {- 1} & {+ j} & {+ 1} & {- j} & {- 1} \\{- 1} & {+ j} & {+ 1} & {+ 1} & {+ 1} & {- j}\end{bmatrix}.}$

FIG. 4I shows eight antenna array patterns for a six-element arrayemploying an element spacing of λ/2 and quadrature beamforming/combiningweights. The codebook comprises the set of eight vectors given by thecolumns of the following weight matrix

${W = \begin{bmatrix}{+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} \\{- 1} & {- j} & {- j} & {- j} & {+ 1} & {+ j} & {+ j} & {+ j} \\{+ 1} & {+ j} & {- 1} & {- j} & {+ 1} & {+ j} & {- 1} & {- j} \\{- 1} & {+ 1} & {+ j} & {- 1} & {+ 1} & {- 1} & {- j} & {+ 1} \\{+ 1} & {- 1} & {+ 1} & {- 1} & {+ 1} & {- 1} & {+ 1} & {- 1} \\{- 1} & {+ j} & {- j} & {+ j} & {+ 1} & {- j} & {+ j} & {- j}\end{bmatrix}},$wherein WW^(H)=8I.

FIG. 4J shows eight antenna array patterns for a seven-element arrayemploying an element spacing of λ/2 and quadrature beamforming/combiningweights. The codebook comprises the set of eight vectors given by thecolumns of the following weight matrix in which the relationshipWW^(H)=8I also holds.

$W = \begin{bmatrix}{+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} \\{- 1} & {- j} & {- j} & {- j} & {+ 1} & {+ j} & {+ j} & {+ j} \\{+ 1} & {+ j} & {- 1} & {- j} & {+ 1} & {+ j} & {- 1} & {- j} \\{- 1} & {+ 1} & {+ j} & {- 1} & {+ 1} & {- 1} & {- j} & {+ 1} \\{+ 1} & {- 1} & {+ 1} & {- 1} & {+ 1} & {- 1} & {+ 1} & {- 1} \\{- 1} & {+ j} & {- j} & {+ j} & {+ 1} & {- 1} & {+ j} & {- j} \\{+ 1} & {- j} & {- 1} & {+ j} & {+ 1} & {- j} & {- 1} & {+ j}\end{bmatrix}$

FIG. 4K shows eight orthogonal antenna array patterns for aneight-element array employing an element spacing of λ/2 and quadraturebeamforming/combining weights. The codebook comprises the set of eightorthogonal vectors given by the columns of the following weight matrix

$W = {\begin{bmatrix}{+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} \\{- 1} & {- j} & {- j} & {- j} & {+ 1} & {+ j} & {+ j} & {+ j} \\{+ 1} & {+ j} & {- 1} & {- j} & {+ 1} & {+ j} & {- 1} & {- j} \\{- 1} & {+ 1} & {+ j} & {- 1} & {+ 1} & {- 1} & {- j} & {+ 1} \\{+ 1} & {- 1} & {+ 1} & {- 1} & {+ 1} & {- 1} & {+ 1} & {- 1} \\{- 1} & {+ j} & {- j} & {+ j} & {+ 1} & {- j} & {+ j} & {- j} \\{+ 1} & {- j} & {- 1} & {+ j} & {+ 1} & {- j} & {- 1} & {+ j} \\{- 1} & {- 1} & {+ j} & {+ 1} & {+ 1} & {+ 1} & {- j} & {- 1}\end{bmatrix}.}$

FIG. 4L shows twelve antenna array patterns for an eight-element arrayemploying an element spacing of λ/2 and quadrature beamforming/combiningweights. The codebook comprises the set of eight vectors given by thecolumns of the following weight matrix

$W = {\begin{bmatrix}{+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} \\{- 1} & {- 1} & {- j} & {- j} & {+ 1} & {- j} & {+ 1} & {+ j} & {+ 1} & {+ j} & {+ j} & {- 1} \\{+ 1} & {+ 1} & {- 1} & {- 1} & {- j} & {- j} & {+ 1} & {+ j} & {+ j} & {- 1} & {- 1} & {+ 1} \\{- 1} & {- j} & {+ 1} & {+ j} & {- 1} & {- j} & {+ 1} & {+ j} & {- 1} & {- j} & {+ 1} & {+ j} \\{+ 1} & {+ j} & {- j} & {+ 1} & {- 1} & {- 1} & {+ 1} & {- 1} & {- 1} & {+ 1} & {+ j} & {- j} \\{- 1} & {+ 1} & {+ j} & {- j} & {+ j} & {- 1} & {+ 1} & {- 1} & {- j} & {+ j} & {- j} & {+ 1} \\{+ 1} & {- 1} & {+ 1} & {- 1} & {+ 1} & {- 1} & {+ 1} & {- 1} & {+ 1} & {- 1} & {+ 1} & {- 1} \\{- 1} & {+ 1} & {- j} & {+ j} & {+ 1} & {+ j} & {+ 1} & {- j} & {+ 1} & {- j} & {+ j} & {+ 1}\end{bmatrix}.}$

FIG. 4M shows sixteen antenna array patterns for an eight-element arrayemploying an element spacing of λ/2 and quadrature beamforming/combiningweights. The codebook comprises the set of eight vectors given by thecolumns of the following weight matrix

${W = \begin{bmatrix}{+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} & {+ 1} \\{- 1} & {- 1} & {- j} & {- j} & {- j} & {- j} & {- j} & {+ 1} & {+ 1} & {+ 1} & {+ j} & {+ j} & {+ j} & {+ j} & {+ j} & {- 1} \\{+ 1} & {+ 1} & {+ j} & {- 1} & {- 1} & {- 1} & {- j} & {+ 1} & {+ 1} & {+ 1} & {+ j} & {- 1} & {- 1} & {- 1} & {- j} & {+ 1} \\{- 1} & {- 1} & {+ 1} & {+ j} & {+ j} & {+ j} & {- 1} & {+ 1} & {+ 1} & {+ 1} & {+ j} & {- j} & {- j} & {- j} & {+ 1} & {- 1} \\{+ 1} & {+ j} & {- 1} & {- j} & {+ 1} & {+ j} & {- 1} & {- j} & {+ 1} & {+ j} & {- 1} & {- j} & {+ 1} & {+ j} & {- 1} & {- j} \\{- 1} & {- j} & {+ j} & {- 1} & {- j} & {+ 1} & {+ j} & {- j} & {+ 1} & {+ j} & {- 1} & {+ 1} & {+ j} & {- 1} & {- j} & {+ j} \\{+ 1} & {+ j} & {- j} & {+ j} & {- 1} & {- j} & {+ j} & {- j} & {+ 1} & {+ j} & {- j} & {+ j} & {- 1} & {- j} & {+ j} & {- j} \\{- 1} & {- j} & {- 1} & {+ 1} & {+ j} & {- 1} & {+ 1} & {- j} & {+ 1} & {+ j} & {+ 1} & {- 1} & {- j} & {+ 1} & {- 1} & {+ j}\end{bmatrix}},$wherein WW^(H)=16I.

Some embodiments of the invention may provide for quasi-omni andcomplementary Golay codebooks employing binary beamforming/combiningweights for antenna arrays having from two to eight antenna elements(N=2 . . . 8). The beamformer weights are +1 or −1. A +1 weight on anantenna element means that +I (a positive in-phase signal) istransmitted on that antenna element, whereas a −1 weight means that −I(a negative in-phase signal) is transmitted on that antenna element.Each codebook may contain multiple options for quasi-omni patterns.Depending on the polar and azimuthal antenna gain patterns, one or morequasi-omni patterns may be used. Real complementary Golay patterns existfor N=2, 4, and 8 only. Depending on the polar and azimuthal antennagain pattern, one or both complementary patterns can be used.

A quasi-omni codebook for a two-element array comprises two orthogonalbeamforming (or combining) vectors given by the columns of the weightmatrix

$W = {\begin{bmatrix}{+ 1} & {+ 1} \\{- 1} & {+ 1}\end{bmatrix}.}$The two complementary Golay patterns g₁(θ,φ) and g₂(θ,φ), whereg₁(θ,φ)+g₂(θ,φ)=2, are shown in FIG. 5A. The first pattern is maximum indirection 0° and has a HPBW of 120.5° and maximum directivity of 3.0 dB.The second pattern is maximum in direction 90° with a HPBW of 60.4° andmaximum directivity of 3.0 dB.

A quasi-omni codebook for a three-element antenna array comprising threequasi-orthogonal beamforming/combining vectors is given by the columnsof weight matrix W

$W = \begin{bmatrix}{+ 1} & {+ 1} & {+ 1} \\{- 1} & {+ 1} & {+ 1} \\{+ 1} & {- 1} & {+ 1}\end{bmatrix}$The resulting quasi-orthogonal beam patterns are shown in FIG. 5B. Thefirst pattern is maximum in direction 0° and has a HPBW of 93.4° andmaximum directivity of 4.77 dB. The second pattern is maximum indirections 60° and 120° with a HPBW of 40.4° and maximum directivity of2.2 dB. The third pattern is maximum in direction 90° and has a HPBW of36.7° and maximum directivity of 4.77 dB.

A pair of Golay complementary patterns g₁(θ,φ)+g₂(θ,φ)=1.77 is shown inFIG. 5C. Two orthogonal beamforming/combining vectors are given by thecolumns of the following weighting matrix for a four-element array

$W = {\begin{bmatrix}{+ 1} & {+ 1} \\{- 1} & {+ 1} \\{+ 1} & {+ 1} \\{+ 1} & {- 1}\end{bmatrix}.}$The first pattern is maximum in directions 46° and 134°, has a HPBW of123.0° and maximum directivity of 2.48 dB. The second pattern is maximumin directions 72° and 108° with a HPBW of 62.9° and maximum directivityof 2.48 dB.

FIG. 5D shows three quasi-orthogonal beam patterns corresponding to acodebook for a five-element array comprising three quasi-orthogonalbeam-forming vectors. The codebook vectors are the columns of thefollowing weighting matrix.

$W = {\begin{bmatrix}{+ 1} & {+ 1} & {+ 1} \\{- 1} & {+ 1} & {+ 1} \\{+ 1} & {- 1} & {+ 1} \\{+ 1} & {+ 1} & {+ 1} \\{+ 1} & {+ 1} & {- 1}\end{bmatrix}.}$The first pattern is maximum in direction 0°, with a HPBW of 109.3° andmaximum directivity of 2.55 dB. The second pattern is maximum indirections 54° and 126°, with a HPBW of 63.5° and maximum directivity of3.25 dB. The third pattern is maximum in directions 79° and 101°, with aHPBW of 43.8° and maximum directivity of 3.22 dB.

FIG. 5E shows three quasi-orthogonal beam patterns corresponding to acode book for a six-element array. The codebook comprises threequasi-orthogonal beam-forming vectors, which are columns of thefollowing weighting matrix.

$W = {\begin{bmatrix}{+ 1} & {+ 1} & {+ 1} \\{- 1} & {+ 1} & {+ 1} \\{+ 1} & {- 1} & {+ 1} \\{- 1} & {+ 1} & {+ 1} \\{+ 1} & {+ 1} & {+ 1} \\{+ 1} & {+ 1} & {- 1}\end{bmatrix}.}$In this case, the first pattern is maximum in directions 23° and 157°,with a HPBW of 88.2° and maximum directivity of 4.30 dB. The secondpattern is maximum in directions 57° and 123°, with a HPBW of 20.0° andmaximum directivity of 5.11 dB. The third pattern is maximum indirections 85° and 95°, with a HPBW of 32.7° and maximum directivity of4.30 dB.

FIG. 5F shows three quasi-orthogonal beam patterns corresponding to acode book for a seven-element array. The codebook comprises threequasi-orthogonal beam-forming vectors, which are columns of thefollowing weighting matrix.

$W = {\begin{bmatrix}{+ 1} & {+ 1} & {+ 1} \\{- 1} & {+ 1} & {- 1} \\{+ 1} & {+ 1} & {- 1} \\{- 1} & {- 1} & {+ 1} \\{- 1} & {- 1} & {+ 1} \\{+ 1} & {+ 1} & {+ 1} \\{+ 1} & {- 1} & {+ 1}\end{bmatrix}.}$The first pattern has a HPBW of 133.3° and maximum directivity of 2.77dB. The second pattern has a HPBW of 109.7° and maximum directivity of1.39 dB. The third pattern has a HPBW of 53.8° and maximum directivityof 2.77 dB.

A quasi-omni codebook for an eight-element array comprises twoorthogonal beamforming (or combining) vectors given by the columns ofthe weight matrix

$W = \begin{bmatrix}{+ 1} & {+ 1} \\{+ 1} & {- 1} \\{- 1} & {- 1} \\{- 1} & {+ 1} \\{+ 1} & {+ 1} \\{- 1} & {+ 1} \\{+ 1} & {+ 1} \\{- 1} & {+ 1}\end{bmatrix}$The two complementary Golay patterns g₁(θ,φ)+g₂(θ,φ)=2 are shown in FIG.5G. The first pattern is maximum in direction 0° and has a HPBW of 98.70and maximum directivity of 3.0 dB. The second pattern is maximum indirection 90° with a HPBW of 40.9° and maximum directivity of 3.0 dB.

A quasi-omni codebook for a two-element array employing quadratureweights is identical to the case in which binary weights are employed.Thus, the codebook comprises two orthogonal beamforming (or combining)vectors given by the columns of the weight matrix

$W = {\begin{bmatrix}{+ 1} & {+ 1} \\{- 1} & {+ 1}\end{bmatrix}.}$The two complementary Golay patterns g₁(θ,φ) and g₂(θ,φ), whereg₁(θ,φ)+g₂(θ,φ)=2, are shown in FIG. 6A. The first pattern is maximum indirection 0° and has a HPBW of 120.5° and maximum directivity of 3.0 dB.The second pattern is maximum in direction 90° with a HPBW of 60.4° andmaximum directivity of 3.0 dB.

FIG. 6B shows a pair of quasi-omni beam patterns of a three-elementarray employing quadrature weights. The codebook comprises the pair ofquadrature vectors derived from the pair of columns in the followingweight matrix

$W = {\begin{bmatrix}{+ 1} & {+ 1} \\{+ j} & {+ 1} \\{+ 1} & {- 1}\end{bmatrix}.}$One pattern has a HPBW of 123.6° and the other pattern has a HPBW of80.0°. Both patterns have a maximum directivity of 2.22 dB.

FIG. 6C is a plot of two Golay complementary patterns g₁(θ,φ) andg₂(θ,φ), where g₁(θ,φ)+g₂(θ,φ)=2, generated by a four-element array withquadrature weights. The resulting quasi-omni codebook for this case isgiven by vectors represented by the columns of the following weightmatrix

$W = {\begin{bmatrix}{+ 1} & {+ 1} \\{- j} & {+ j} \\{+ j} & {+ j} \\{- 1} & {+ 1}\end{bmatrix}.}$The first pattern is maximum in direction 0° and has a HPBW of 83.4° andmaximum directivity of 3.01 dB. The second pattern is maximum indirection 90° with a HPBW of 29.4° and maximum directivity of 3.01 dB.

FIG. 6D shows a quasi-omni pattern with maximum directivity of 2.55 dBgenerated by a five-element array employing a weight vector w=[+1 −1 +1+1 +1], which is the quasi-omni codebook for this case.

FIGS. 7A-7D show quasi-omni beam patterns for a six-element arraycorresponding to vectors of a quasi-omni codebook, wherein each vectoris a column of the following weight matrix

$W = {\begin{bmatrix}{+ 1} & {+ 1} & {+ 1} & {+ 1} \\{- 1} & {- 1} & {+ 1} & {+ 1} \\{+ j} & {- j} & {- j} & {+ j} \\{- 1} & {- 1} & {- 1} & {- 1} \\{+ j} & {- j} & {+ 1} & {+ 1} \\{+ j} & {- j} & {- 1} & {- 1}\end{bmatrix}.}$The quasi-omni beam patterns shown in FIGS. 7A and 7B have maximumdirectivity of 2.39 dB, and the quasi-omni patterns shown in FIGS. 7Cand 7D have maximum directivity of 2.86 dB.

A six-element array is configured to generate the pair of Golaycomplementary patterns g₁(θ,φ) and g₂(θ,φ), where g₁(θ,φ)+g₂(θ,φ)=1.93,shown in FIG. 8A. A related pair of orthogonal beamforming/combiningvectors comprises the columns of the following weight matrix

$W = {\begin{bmatrix}{+ 1} & {+ 1} \\{- j} & {+ j} \\{- j} & {- j} \\{- j} & {+ j} \\{+ 1} & {+ 1} \\{+ j} & {- j}\end{bmatrix}.}$The first pattern is maximum in directions 31° and 149°, has a HPBW of120.7° and maximum directivity of 2.86 dB. The second pattern is maximumin directions 82° and 98° with a HPBW of 61.2° and maximum directivityof 2.86 dB.

FIG. 8B shows three quasi-omni beam patterns from a seven-element arraywith quadrature weighting vectors. The vectors are components of aquasi-omni codebook and include the columns of the following weightmatrix

$W = {\begin{bmatrix}{+ 1} & {+ 1} & {+ 1} \\{+ j} & {+ 1} & {- 1} \\{- 1} & {+ 1} & {- 1} \\{+ j} & {- 1} & {+ 1} \\{- 1} & {- 1} & {+ 1} \\{+ j} & {+ 1} & {+ 1} \\{+ 1} & {- 1} & {+ 1}\end{bmatrix}.}$The maximum directivity of the first two patterns is 1.39 dB, and themaximum directivity of the third pattern is 2.77 dB.

An eight-element array can employ a codebook comprising a pair ofquadrature weight vectors (expressed by columns of the following weightmatrix) to produce two complementary beam patterns shown in FIG. 8C.

$W = \begin{bmatrix}{+ 1} & {+ 1} \\{+ 1} & {- 1} \\{- 1} & {- 1} \\{- 1} & {+ 1} \\{+ 1} & {+ 1} \\{- 1} & {+ 1} \\{+ 1} & {+ 1} \\{- 1} & {+ 1}\end{bmatrix}$Both patterns have maximum directivity of 3.0 dB. One pattern is maximumin direction 0° and has a HPBW of 98.7°, and the other pattern ismaximum in direction 90° and has a HPBW of 40.9°.

A pair of orthogonal beamforming/combining vectors (shown in FIGS. 8Dand 8E) may also be generated for an eight-element array using thefollowing weight matrix

$W = \begin{bmatrix}{+ 1} & {+ 1} \\{+ 1} & {- 1} \\{- 1} & {+ 1} \\{+ 1} & {+ 1} \\{- 1} & {+ 1} \\{+ 1} & {+ 1} \\{+ 1} & {+ 1} \\{+ 1} & {- 1}\end{bmatrix}$

Some embodiments of the invention may employ a sectored antenna array(SEAA) or a switched antenna array (SWAA). The codebook for an N-elementSEAA or SWAA may be expressed by an identity matrix:

$W = \begin{bmatrix}1 & 0 & \cdots & 0 \\0 & 1 & \ddots & \vdots \\\vdots & \ddots & \ddots & 0 \\0 & \cdots & 0 & 1\end{bmatrix}$Each beamforming vector has only one non-zero entry since only oneantenna element is active at a time.

One embodiment of the invention provides for a unified messagingprotocol that is independent of antenna configuration and estimationalgorithms employed for beamforming (i.e., estimating w and c). Themessaging protocol may be configured to support a variety of antennaconfigurations used for transmitting and receiving. Such configurationsmay include beamforming antenna arrays, such as phased arrays. Antennaconfigurations may include sectored and switched antenna arrays. Antennaconfiguration may be defined by a variety of beam patterns, includingomni, quasi-omni, or directional single antenna. The messaging protocolalso supports SAS and AAS configurations, and it may be configured tosupport proactive and on-demand beamforming. In one embodiment, themessaging protocol is further configured to support a variety of linkmodels, including (but not limited to) per-packet beamforming between apiconet controller and multiple subscriber devices, a link between apiconet controller and a single subscriber device, and peer-to-peerlinks between subscriber devices.

Embodiments of the invention may provide for a plurality of beamformingprotocols to be implemented, including a proactive beamforming protocoland an on-demand beamforming protocol. Proactive beamforming isperformed using the beacon portion of a superframe (such as shown inFIG. 9) and is used when the piconet controller is the data source forone or more subscriber devices. For example, the piconet controller maybe a Kiosk, STB, or Laptop computer, and it is configured to send eachpacket in at least one of a plurality of different directions to thedestination device.

On-demand beamforming may be employed for transmissions between twosubscriber devices or between a piconet controller and one subscriberdevice. On-demand beamforming employs the Channel Time Allocation (CTA)part of the superframe (such as shown in FIG. 9) allocated to the pairof transceivers. In both beamforming protocols, quasi-omni transmissionsconvey information about the structure of the directional trainingsections, and the directional training sections enable CSI acquisitionand tracking.

The piconet controller beacon comprises at least one quasi-omni (Q-omni)section and at least one directional section. In one embodiment, theQ-omni section has L identical Q-omni sub-beacons (S-beacons) coveringdifferent (and possibly overlapping) geographical areas around thepiconet controller. The aggregated coverage of the Q-omni S-beaconscovers the target space around the piconet controller. Each Q-omniS-beacon is transmitted using a different Q-omni beamforming patternselected from a Q-omni codebook.

In the embodiment shown in FIG. 9, the directional section may compriseN repetitions of a training sequence (i.e., a plurality N of directionaltraining segments) where each repetition is transmitted by the piconetcontroller with a different orthogonal or quasi-orthogonal beamformingvector from an orthogonal (or quasi-orthogonal) codebook. In this case,the directional training segments are sent back-to-back, except for asmall guard interval. However, alternative embodiments of the inventionmay provide for interleaving (or otherwise positioning) Q-omni trainingsegments within the directional section. For example, a Q-omni trainingsegment may have the same format as a directional training segment, butit is sent omni-directionally. In one embodiment, a Q-omni trainingsegment follows each directional training segment. A subscriber deviceuses the Q-omni training segments to help compensate for timing andfrequency drift, as such compensation is necessary for generatingaccurate estimates of the CSI.

The Contention Access Period (CAP) is divided into L identical periodsreferred to as Sub-CAPs (S-CAPs). The L S-CAPs correspond to the LQ-omni beacons. During the l^(th) S-CAP, the piconet controller is in areceiving mode using the same Q-omni beamformer vector it used fortransmission during the l^(th) Q-Omni beacon.

FIG. 10A shows the packet structure of an S-beacon for OFDM, and FIG.10B shows the packet structure of an S-beacon for Single Carrier (SC)signaling. Depending on the antenna gain of the Q-omni beacon, thepiconet controller may adjust the length of the SYNC, the data rate inthe header, and the PSDU fields.

The number L of Q-omni S-beacons may be reduced in order to reduceoverhead. For a single antenna, L=1. For SAA, L is the number of sector(or switched) antennas. In beamforming or phased-array configurations, Lequals 1 or 2, but it may be more. During transmission, the piconetcontroller employs L Quasi-omni beamforming vectors from a correspondingquasi-omni codebook, and one Q-omni beamforming vector is used perQ-omni sub-beacon transmission.

In one embodiment of the invention, L=1 for a transmitting phased arraywith six elements, which employs a one-dimensional vector w=[+1 −1 +j −1+j +j]^(T) to transmit the Q-omni sub-beacon. In a different embodiment,L=2 for a two-dimensional phased antenna array wherein N_(x)=4 andN_(y)=3. The first Q-omni sub-beacon is transmitted using thebeamforming matrix, W_(xy,11)=w_(x,1)w_(y,1) ^(T), where w_(x,1)=[+1 −j+j −1]^(T), and w_(y,1)=[+1 +1 −1]^(T). The second Q-omni sub-beacon istransmitted using the beamforming matrix, W_(xy,21)=w_(x,2)w_(y,1) ^(T),where w_(x,2)=[+1 +j +j +1]^(T) and w_(y,1)=[+1 +1 −1]^(T).

The directional section of the frame shown in FIG. 9 comprises Nrepetitions of a training sequence. FIG. 11A illustrates a short OFDMtraining sequence. FIG. 11B shows a long OFDM training sequence. FIG.11C shows a short single-carrier training sequence. FIG. 11D shows along single carrier training sequence. The sequences denoted by vectorsu₅₁₂, v₅₁₂, and s₅₁₂ are described in Provisional Application Ser. No.60/985,957, filed Nov. 6, 2007, which is incorporated by reference inits entirety.

The training sequence includes N_(s) repetitions (where N_(s) may bezero) of a sync sequence s followed by N_(c) (e.g., one or two)repetitions of the CES field. Each training sequence transmitted by apiconet controller employs a different orthogonal (or quasi-orthogonal)beam pattern selected from an orthogonal (or quasi-orthogonal) codebook.In the case where OFDM and single-carrier employ short trainingsequences, the two sync sequence may be used for automatic gain control(AGC). Furthermore, the CES field may be used to acquire the CSI. Amatched-filter receiver may align and add the outputs of a Golay matchedfilter configured to correlate the received signal with the modifiedGolay sequences u and v to produce a perfect channel estimate. Also, thereceiver may produce a difference signal, which provides a perfect noiseestimate.

In one embodiment, a beamforming antenna array with N_(x)=4 and N_(y)=2.employs a length-4 x-axis codebook:

$\begin{matrix}{W = \begin{bmatrix}w_{x,1} & w_{x,2} & w_{x,3} & w_{x,4}\end{bmatrix}} \\{= \begin{bmatrix}{+ 1} & {+ 1} & {+ 1} & {+ 1} \\{- 1} & {- j} & {+ 1} & {+ j} \\{+ 1} & {- 1} & {+ 1} & {- 1} \\{- 1} & {+ j} & {+ 1} & {- j}\end{bmatrix}}\end{matrix}$The corresponding length-2 y-axis codebook is

${W_{y} = {\begin{bmatrix}w_{y,1} & w_{y,2}\end{bmatrix} = \begin{bmatrix}{+ 1} & {+ 1} \\{- 1} & {+ 1}\end{bmatrix}}},$wherein the total number of orthogonal beamforming matrices is J=8, i.e.W_(xy,mn)=W_(x,m)W_(y,n) ^(T), where m=1, . . . , 4 and n=1, 2:

${W_{{xy},11} = \begin{bmatrix}{+ 1} & {- 1} \\{- 1} & {+ 1} \\{+ 1} & {- 1} \\{- 1} & {+ 1}\end{bmatrix}},{W_{{xy},12} = \begin{bmatrix}{+ 1} & {+ 1} \\{- 1} & {- 1} \\{+ 1} & {+ 1} \\{- 1} & {- 1}\end{bmatrix}},\ldots\;,{W_{{xy},42} = {\begin{bmatrix}{+ 1} & {- 1} \\{+ j} & {- j} \\{- 1} & {+ 1} \\{- j} & {+ j}\end{bmatrix}.}}$In this case, the piconet controller completes a cycle of training bytransmitting J=8 training sequences, each one being sent in a differentdirection as specified by the beamforming matrices W_(xy,11), W_(xy,12),. . . , W_(xy4,2). For example, the first training sequence is sent inthe direction corresponding to beamforming matrix W_(xy,11), the secondtraining sequence is sent in the direction corresponding to beamformingmatrix W_(xy,12), etc.

In some embodiments, the piconet controller may be configured to employonly a subset of the available beamforming matrices. For example, thepiconet controller may transmit over a restricted angular range (e.g.,180°, instead of 360°). The piconet controller employs a directionalcodebook, which is the subset of possible beamforming matrices that thepiconet controller could use to train the subscriber devices. If thedirectional codebook is of size J, a transmission of J trainingsequences in the corresponding J directions is referred to as a cycle.In some embodiments, the L identical Q-omni S-beacons may includeindices of the codebook vectors selected by the piconet controller. TheQ-omni S-beacons may also convey the number of cycles per superframeand/or the number of superframes per cycle.

FIG. 12A shows a superframe comprising M cycles, whereas FIG. 12B showsa cycle occurring every M superframes. A subscriber device is configuredto listen to the Q-omni transmissions from a piconet controller. Upondetection, the subscriber device decodes the content of the Q-omniS-beacon to obtain the structure of the directional section. Thesubscriber device selects a first codebook vector to steer its antennato a first direction. The subscriber device selects a second codebookvector to steer its antenna to a second direction, and it may repeatthis procedure for each codebook vector. Alternatively, the subscriberdevice may select codebook vectors from a subset of the codebook. Thesubscriber device calculates the CSI matrix, H, from which it estimatesthe optimal beamforming weights for the piconet controller and theoptimal combining vector for itself. In the SAS case, the subscriberdevice may listen to the Q-omni transmissions until it determines acombination of weights that it deems to provide adequate link quality.The resulting beamforming weights are transmitted back to the piconetcontroller.

FIG. 13A shows a beamforming information element of a transmission framecomprising training sequence information, antenna array informationabout the transmit and receive antennas, antenna type, a Q-Omni S-beaconidentifier, and the number of Q-Omni S-beacons. The antenna type mayinclude information about the piconet controller antenna (e.g., singleantenna, beamforming array, phased array, SEAA, SWAA), SAS or AASantenna configuration, and whether quadrature or binary weights are usedfor the transmit and receive sides. The fields of the beamforminginformation element may be adapted for different antenna configurations.For example, the training sequence information and the antenna arrayinformation may be omitted for a single antenna configuration or aswitched antenna array.

FIG. 13B shows the antenna array information portion of the beamforminginformation element. This information may include the number N_(x) ofantennas along the x-axis, ID of the codebook used along the x-axis, thenumber N_(y) of antennas along the y-axis, and ID of the codebook usedalong the y-axis in the case of a two-dimensional array. Someembodiments may include the size J_(x) and ID of the subset of thebeamforming vectors to be used along the x-axis, and the size J_(y) andID of the subset of the beamforming vectors to be used along the y-axis.

FIG. 13C shows the training sequence information portion of thebeamforming information element, which includes the guard intervalduration in units of 32×T_(c) (where T_(c) is the chip or samplingduration), the number of CES repetitions, N_(c), and the number of SYNCrepetitions, N_(s), and the number of training sequence repetitions.

FIG. 16A illustrates a method for performing proactive beamforming. Apiconet controller transmits 1601 a number L of Q-omni S-beacons and anumber N of directional training sequences per superframe. A subscriberdevice listens to and decodes 1602 at least one of the Q-omni S-beacons,from which it acquires information related to the directional section.In one embodiment of the invention, the subscriber device may listen tothe entire set of Q-omni S-beacons. The subscriber device selects 1603an appropriate subset of an orthogonal (or quasi-orthogonal) codebookand begins a scanning procedure using the selected combining vectors.

In one embodiment, when the subscriber device steers to a particulardirection using a vector from the codebook and listens to a transmittedcycle, it may store a Link quality Factor (LQF). This process isrepeated until the subscriber device finds an l^(th) LQF above apredetermined threshold, or until it has finished listening to all thecodebook vectors and acquires the CSI matrix.

The subscriber device estimates 1604 its optimal combining vector c₂ andan optimal beamforming vector w₁ for the piconet controller. Theestimated optimal beamforming vector w₁ (and optionally, the optimalcombiner vector c₂) are fed back 1605 to the piconet controller duringthe l^(th) S-CAP.

In the SAS case, the subscriber device and the piconet controllerexchange 1606 data packets during a CTAP. The subscriber device maytrack 1607 the beamforming and combining vectors by periodicallyscanning the beacon. The subscriber device may periodically feed back1608 any updates to w and c.

In the AAS case, steps 1606-1608 are bypassed. Instead, on-demandbeamforming may be used during the CTAP allocated to the communicationlink in order to complete bi-directional beamforming. As shown in FIG.16B, the piconet controller acquires 1616 the uplink CSI, H_(2→1)(n) forn=0, 1, . . . , N−1, to estimate its optimal combining vector c₁ and thesubscriber device's optimal beamforming vector w₂, and then conveys 1617at least the beamforming weight vector w₂ to the subscriber device. Onceacquisition is complete, the subscriber device may transmit 1618 aninfrequent “directional acquisition period” (e.g., once every fewmicroseconds) to allow the piconet controller to track and update w₂ andc₁. The update rate (tracking rate) depends on the maximum Doppler thatthe system can tolerate. For a pedestrian speed of 3 m/s at 60 GHz, theDoppler frequency is f_(d)=600 Hz, and the coherence time isapproximately 0.3 ms, which allows an update rate of once every 0.3 msor less.

On-demand beamforming (which is performed between two subscriber devicesor between a piconet controller and one subscriber device) employs theChannel Time Allocation (CTA) part of the superframe shown in FIG. 14A.FIG. 17A is a flow diagram of an on-demand beamforming method for SAS inaccordance with one embodiment of the invention. Antenna information isexchanged 1701 during association such that each transceiver knows theantenna array processing capabilities (e.g., number of array elements,range of antenna-element weights, etc.) of the other transceiver(s).Quasi-omni acquisition 1702 is performed as a first transceivertransmits a Q-omni S-beacon to a second transceiver. Directionalacquisition 1703 is performed as the first transceiver transmits adirectional training sequence to the second transceiver. Onceacquisition is complete, the system may perform tracking 1704 as thefirst transceiver transmits data to the second transceiver.

FIG. 17B illustrates steps of an on-demand beamforming method for AAS inaccordance with an embodiment of the invention. Antenna information isexchanged 1701 during association. Quasi-omni acquisition 1702 isperformed as a first transceiver transmits a Q-omni S-beacon to a secondtransceiver. Directional acquisition 1703 is performed as the firsttransceiver transmits a directional training sequence to the secondtransceiver. Quasi-omni acquisition 1712 is performed as the secondtransceiver transmits a Q-omni S-beacon to the first transceiver.Similarly, directional acquisition 1713 is performed as the secondtransceiver transmits a directional training sequence to the firsttransceiver. Once acquisition in both directions is complete, the systemmay perform tracking 1714 as the first transceiver transmits data to thesecond transceiver and/or the second transceiver transmits data to thefirst transceiver.

FIG. 14B illustrates a quasi-omni acquisition signaling protocol inaccordance with an embodiment of the invention. In a CTA frame (shown inFIG. 14A), a first transceiver transmits a number L of quasi-omnipackets carrying the beamforming information element. Each of the Ltransmissions is followed by L listening periods (ACKs). The firsttransceiver continues repeating this structure until it receives an ACKin one of the L listening periods (e.g., at the l^(th) listeningperiod). From this point on, the first transceiver selects the l^(th)Q-omni direction for transmission (which is also the reception directionin the SAS case) from the Q-omni codebook. The second transceiverrecords its best Q-omni receiving direction (which is also the besttransmitting direction in SAS case) and uses it for any future Q-omnireception. In the AAS case, the process is repeated as the secondtransceiver transmits to the first transceiver.

FIG. 15 illustrates a frame format for directional training employingperiodic transmissions from the first transceiver to the secondtransceiver, and FIG. 18A illustrates a method in accordance with anembodiment of the invention that employs the frame format. A directionalacquisition period may comprise an optional Q-omni packet followed by alistening period. One cycle of directional training sequencestransmitted by the first transceiver corresponds to all J orthogonal(quasi-orthogonal) beamforming vectors from a subset of the selectedcodebook. Each cycle is followed by a listening period (ACK) to listento any feedback from the second transceiver.

The first transceiver repeats the period 1801 until the secondtransceiver acquires the CSI, H_(1→2)(n) for n=0, 1, . . . , N−1, orfinds an adequate link-quality indicator (LQI) 1802. The secondtransceiver estimates preferred w₁ and c₂ 1803 and couples at least thew₁ estimate to the first transceiver 1804 during the listening (ACK)period. The preferred beamforming vector w₁ may be one of thetransceiver's codebook vectors, or it may be a linear combination of thecodebook vectors, or it may be unrelated to the transceiver's codebookvectors.

In one embodiment employing a four-element array with a codebookrepresented by the following weight matrix

${W = \begin{bmatrix}{+ 1} & {+ 1} & {+ 1} & {+ 1} \\{- 1} & {- j} & {+ 1} & {+ j} \\{+ 1} & {- 1} & {+ 1} & {- 1} \\{- 1} & {+ j} & {+ 1} & {- j}\end{bmatrix}},$the codebook may comprise one or more of the vectors [1 −1 1 −1], [1 −j−1 j], [1 1 1 1], and [1 j −1 −j]. If the optimal beamforming/combiningvector is chosen from one of the codebook vectors, the embodiment isreferred to as beam-switching.

In one embodiment, the optimal beamforming/combining vector is selectedfrom any of the possible weight combinations for the four-element array.If quadrature weights are employed (i.e., weights ±1 and ±j), then thereare 4⁴ possible combinations from which to select the vector. Oneembodiment of the invention provides for selecting an optimalbeamforming/combining vector from weights comprising any phasor. Anotherembodiment may employ weights comprising a range of amplitudes andphases.

The transceivers will employ the w₁ and c₂ estimates for beamforming andcombining during data communications. Either or both transceivers mayupdate 1805 the estimates w₁ and c₂ when the first transceiver transmitsa directional acquisition period.

For the AAS case, additional steps shown in FIG. 18B are performed. Thesecond transceiver transmits directional training sequences 1811 to thefirst transceiver, and the first transceiver acquires the CSI, H_(2→1)(or determines an adequate LQI) 1812. The first transceiver estimates w₂and c₁ 1813 and couples at least the w₂ estimate 1814 to the secondtransceiver. The estimates w₁ and c₂ are employed as beamforming andcombining weights during data transmission, and these estimates w₁ andc₂ may be updated periodically 1815 when the second transceivertransmits a directional acquisition period.

The scope of the invention should not be interpreted as being limited tothe array-processing embodiments illustrated herein. Rather, theApplicants anticipate that alternative embodiments may comprise antennaarrays with more than eight elements along a particular axis and antennaarrays comprising antennas with a plurality of polarizations, and thatsuch antenna-array configurations fall within the scope and spirit ofthe invention. In one embodiment, two dipole antennas with orthogonallinear polarizations may be employed together to produce a quasi-omnipattern.

It should be appreciated that the apparatus and method embodiments ofthe invention may be implemented using a variety of hardware andsoftware. For example, beamforming, combining, and related applicationsin accordance with embodiments of the invention may be implemented usingspecial-purpose hardware, such as an application specific integratedcircuit (ASIC) and programmable logic devices such as gate arrays,and/or software or firmware running on a computing device, such as amicroprocessor, microcontroller or digital signal processor (DSP). Italso will be appreciated that although functions ofbeamforming/combining weight calculation and selection may be integratedin a single device, such as a single ASIC, they may also be distributedamong several devices.

The invention is not intended to be limited to the preferredembodiments. Furthermore, those skilled in the art should recognize thatthe method and apparatus embodiments described herein may be implementedin a variety of ways, including implementations in hardware, software,firmware, or various combinations thereof. Examples of such hardware mayinclude ASICs, Field Programmable Gate Arrays, general-purposeprocessors, DSPs, and/or other circuitry. Software and/or firmwareimplementations of the invention may be implemented via any combinationof programming languages, including Java, C, C++, Matlab™, Verilog,VHDL, and/or processor specific machine and assembly languages.

Various digital computer system configurations can be employed toperform the method embodiments of this invention, and to the extent thata particular system configuration is capable of performing the methodembodiments of this invention, it is equivalent to the representativesystem embodiments of the invention disclosed herein, and within thescope and spirit of this invention.

Once digital computer systems are programmed to perform particularfunctions pursuant to instructions from program software that implementsthe method embodiments of this invention, such digital computer systemsin effect become special-purpose computers particular to the methodembodiments of this invention. The techniques necessary for thisprogramming are well known to those skilled in the art of computersystems.

Various embodiments of the invention may include variations in systemconfigurations and the order of steps in which methods are performed. Inmany cases, multiple steps and/or multiple components may beconsolidated.

The method and system embodiments described herein merely illustrateparticular embodiments of the invention. It should be appreciated thatthose skilled in the art will be able to devise various arrangements,which, although not explicitly described or shown herein, embody theprinciples of the invention and are included within its spirit andscope. Furthermore, all examples and conditional language recited hereinare intended to be only for pedagogical purposes to aid the reader inunderstanding the principles of the invention. This disclosure and itsassociated references are to be construed as being without limitation tosuch specifically recited examples and conditions. Moreover, allstatements herein reciting principles, aspects, and embodiments of theinvention, as well as specific examples thereof, are intended toencompass both structural and functional equivalents thereof.Additionally, it is intended that such equivalents include bothcurrently known equivalents as well as equivalents developed in thefuture, i.e., any elements developed that perform the same function,regardless of structure.

It should be appreciated by those skilled in the art that the blockdiagrams herein represent conceptual views of illustrative circuitry,algorithms, and functional steps embodying principles of the invention.Similarly, it should be appreciated that any flow charts, flow diagrams,signal diagrams, system diagrams, codes, and the like represent variousprocesses that may be substantially represented in computer-readablemedium and so executed by a computer or processor, whether or not suchcomputer or processor is explicitly shown.

The functions of the various elements shown in the drawings, includingfunctional blocks labeled as “processors” or “systems,” may be providedthrough the use of dedicated hardware as well as hardware capable ofexecuting software in association with appropriate software. Whenprovided by a processor, the functions may be provided by a singlededicated processor, by a shared processor, or by a plurality ofindividual processors, some of which may be shared. Moreover, explicituse of the term “processor” or “controller” should not be construed torefer exclusively to hardware capable of executing software, and mayimplicitly include, without limitation, digital signal processor (DSP)hardware, read-only memory (ROM) for storing software, random accessmemory (RAM), and non-volatile storage. Other hardware, conventionaland/or custom, may also be included. Similarly, the function of anycomponent or device described herein may be carried out through theoperation of program logic, through dedicated logic, through theinteraction of program control and dedicated logic, or even manually,the particular technique being selectable by the implementer as morespecifically understood from the context.

Any element expressed herein as a means for performing a specifiedfunction is intended to encompass any way of performing that functionincluding, for example, a combination of circuit elements which performsthat function, or software in any form, including, therefore, firmware,micro-code or the like, combined with appropriate circuitry forexecuting that software to perform the function. Embodiments of theinvention as described herein reside in the fact that thefunctionalities provided by the various recited means are combined andbrought together in the manner which the operational descriptions callfor. Applicant regards any means that can provide those functionalitiesas equivalent to those shown herein.

1. A beamforming method between a first transceiver and a secondtransceiver, the method comprising: acquiring channel state information(CSI) by transmitting a signal employing at least a subset of abeamforming codebook from the first transceiver to the secondtransceiver and configuring the second transceiver to employ at least asubset of a combining codebook to acquire the CSI, estimating an optimalbeamforming vector and an optimal combining vector from the CSI toproduce an estimated optimal beamforming vector and an estimated optimalcombining vector, and sending at least one of the estimated optimalbeamforming vector and the estimated optimal combining vector to thefirst transceiver.
 2. The method recited in claim 1, wherein estimatingemploys at least one optimality criterion of a set of optimalitycriteria, the set comprising an effective signal-to-noise ratio (SNR)and a mean SNR.
 3. The method recited in claim 1, further comprisingproviding for updating the CSI after the CSI is acquired by transmittingthe subset of the beamforming codebook at a lower rate than a rateemployed for acquiring the CSI and repeating the estimating step and thesending step.
 4. The method recited in claim 1, wherein the beamformingcodebook and the combining codebook comprise at least one of a set ofweight vectors, the set comprising at least one binary weight vector, atleast one quadrature weight vector.
 5. The method recited in claim 1,wherein the beamforming codebook and the combining codebook comprise atleast one of a set of codebooks, the set comprising a quasi-omnicodebook and a complementary Golay codebook.
 6. A method for employing aframe format for signaling between a first transceiver and at least asecond transceiver to select beamforming and combining weights, themethod comprising: transmitting a signal from the first transceiver tothe second transceiver, the signal comprising a plurality oftransmission segments, wherein each of the plurality of transmissionsegments is transmitted with a different beam pattern from apredetermined beamforming codebook, listening for feedback from the atleast second transceiver, and selecting at least one vector of a setbased on feedback from the at least second transceiver, the setcomprising at least one of beamforming weights and combining weights. 7.The method recited in claim 6, wherein transmitting the signal comprisestransmitting at least one of a quasi-omni section and a directionalsection.
 8. The method recited in claim 6, further configured to performat least one of proactive beamforming and on-demand beamforming.
 9. Themethod recited in claim 6, wherein the predetermined beamformingcodebook comprises at least one of a quasi-omni codebook and acomplementary Golay codebook.
 10. The method, recited in claim 6,wherein the predetermined beamforming codebook comprises a subset of atleast one of a quasi-omni codebook and a complementary Golay codebook.11. The method recited in claim 6, wherein listening comprises employinga plurality of combining vectors for listening over a plurality oflistening segments, the plurality of combining vectors being vectors ofthe beamforming codebook, each of the plurality of combining vectorscorresponding to each one of the plurality of transmission segments. 12.The method recited in claim 6, wherein the signal comprises at least oneof a quasi-omni sub-beacon and a directional training sequence.
 13. Amethod for selecting beamforming and combining weights for at least afirst transceiver comprising an antenna array communicatively coupled toa second transceiver comprising an antenna array, the method comprising:receiving a signal at the second transceiver transmitted by the firstwireless transceiver, the signal comprising a plurality of transmissionsegments wherein each of the plurality of transmission segments istransmitted with a different beam pattern from a predeterminedbeamforming codebook, estimating a preferred beamforming vector for thefirst transceiver from at least a subset of the plurality oftransmission segments, estimating a preferred combining vector for thesecond transceiver, and sending at least one of the preferredbeamforming vector and the preferred combining vector to the firsttransceiver during a listening period.
 14. The method recited in claim13, wherein at least one of estimating the preferred beamforming vectorand estimating the preferred combining vector comprises at least one ofacquiring channel state information and calculating a link-qualityindicator.
 15. The method recited in claim 13, wherein estimating thepreferred combining vector comprises correlating the signal with aplurality of Golay sequences to produce a plurality of matched-filteroutputs, and combining the matched-filter outputs to produce a channelestimate.
 16. The method recited in claim 13, wherein the listeningperiod comprises a plurality of listening-period segments, each of theplurality of listening-period segments corresponding to one of theplurality of transmission segments, wherein sending is furtherconfigured for selecting a particular one of the plurality oflistening-period segments corresponding to a particular one of thetransmission segments that corresponds to the estimated preferredbeamforming vector.
 17. The method recited in claim 13, configured forperforming at least one of proactive beamforming and on-demandbeamforming.
 18. The method recited in claim 13, wherein the signalcomprises at least one of a quasi-omni sub-beacon and a directionaltraining sequence.
 19. The method recited in claim 13, whereinestimating the preferred beamforming vector employs a first set ofconstraints corresponding to the first transceiver, and estimating thepreferred combining vector employs a second set of constraintscorresponding to the second transceiver.
 20. The method recited in claim13, wherein the preferred beamforming vector and the preferred combiningvector comprise at least one of a plurality of phases and a plurality ofamplitudes.
 21. The method recited in claim 13, wherein at least one ofthe antenna array of the first transceiver and the antenna array of thesecond transceiver comprises a plurality of antennas, wherein each ofthe plurality of antennas has a different polarization.
 22. An apparatusfor beamforming, the apparatus comprising: a receiver configured toacquire channel state information (CSI) from reception of a signalemploying at least a subset of a beamforming codebook and employment ofat least a subset of a combining codebook; a processor configured toestimate an optimal beamforming vector and an optimal combining vectorfrom the CSI to produce an estimated optimal beamforming vector and anestimated optimal combining vector; and a transmitter configured to sendat least one of the estimated optimal beamforming vector and theestimated optimal combining vector.
 23. An apparatus for beamforming,the apparatus comprising: means for acquiring channel state information(CSI) by transmitting a signal employing at least a subset of abeamforming codebook from the first transceiver to the secondtransceiver and configuring the second transceiver to employ at least asubset of a combining codebook to acquire the CSI; means for estimatingan optimal beamforming vector and an optimal combining vector from theCSI to produce an estimated optimal beamforming vector and an estimatedoptimal combining vector; and means for sending at least one of theestimated optimal beamforming vector and the estimated optimal combiningvector to the first transceiver.
 24. A computer program product forcommunication comprising a computer readable medium comprisinginstructions that when executed cause an apparatus to: acquire channelstate information (CSI) by transmitting a signal employing at least asubset of a beamforming codebook from the first transceiver to thesecond transceiver and configuring the second transceiver to employ atleast a subset of a combining codebook to acquire the CSI; estimate anoptimal beamforming vector and an optimal combining vector from the CSIto produce an estimated optimal beamforming vector and an estimatedoptimal combining vector; and send at least one of the estimated optimalbeamforming vector and the estimated optimal combining vector to thefirst transceiver.
 25. A subscriber device comprising: one or moreantennas; a receiver configured to acquire channel state information(CST) from reception, via the one or more antennas, of a signalemploying at least a subset of a beamforming codebook and employment ofat least a subset of a combining codebook; a processor configured toestimate an optimal beamforming vector and an optimal combining vectorfrom the CSI to produce an estimated optimal beamforming vector and anestimated optimal combining vector; and a transmitter configured tosend, via the one or more antennas, at least one of the estimatedoptimal beamforming vector and the estimated optimal combining vector.26. An apparatus for beamforming, the apparatus comprising: atransmitter configured to transmit a signal comprising a plurality oftransmission segments, wherein each of the plurality of transmissionsegments is transmitted with a different beam pattern from apredetermined codebook; a receiver configured to receive feedback fromat least one transceiver; and a processor configured to select at leastone vector of a set based on feedback from the at least one transceiver,the set comprising at least one of beamforming weights and combiningweights.
 27. An apparatus for beamforming, the apparatus comprising:means for transmitting a signal comprising a plurality of transmissionsegments, wherein each of the plurality of transmission segments istransmitted with a different beam pattern from a predeterminedbeamforming codebook; means for listening for feedback from the at leastone transceiver; and means for selecting at least one vector of a setbased on feedback from the at least one transceiver, the set comprisingat least one of beamforming weights and combining weights.
 28. Acomputer program product for communication comprising a computerreadable medium comprising instructions that when executed cause anapparatus to: transmit a signal comprising a plurality of transmissionsegments wherein each of the plurality of transmission segments istransmitted with a different beam pattern from a predeterminedbeamforming codebook; listening for feedback from the at least onetransceiver; and select at least one vector of a set based on feedbackfrom the at least one transceiver, the set comprising at least one ofbeamforming weights and combining weights.
 29. A piconet controllercomprising: one or more antennas; a transmitter configured to transmit,via the antennas, a signal comprising a plurality of transmissionsegments, wherein each of the plurality of transmission segments istransmitted with a different beam pattern from a predetermined codebook;a receiver configured to receive, via the antennas, feedback from atleast one transceiver; and a processor configured to select at least onevector of a set based on feedback from the at least one transceiver, theset comprising at least one of beamforming weights and combiningweights.
 30. An apparatus for beamforming, the apparatus comprising: areceiver configured to receive a signal comprising a plurality oftransmission segments wherein each of the plurality of transmissionsegments is transmitted with a different beam pattern from apredetermined beamforming codebook; a processor configured to estimate apreferred beamforming vector from at least a subset of the plurality oftransmission segments and estimate a preferred combining vector; and atransmitter configured to send at least one of the preferred beamformingvector and the preferred combining vector during a listening period. 31.An apparatus for beamforming, the apparatus comprising: means forreceiving a signal comprising a plurality of transmission segmentswherein each of the plurality of transmission segments is transmittedwith a different beam pattern from a predetermined beamforming codebook;means for estimating a preferred beamforming vector from at least asubset of the plurality of transmission segments and a preferredcombining vector for the second transceiver; and means for sending atleast one of the preferred beamforming vector and the preferredcombining vector during a listening period.
 32. A computer programproduct for communication comprising a computer readable mediumcomprising instructions that when executed cause an apparatus to:receive a signal comprising a plurality of transmission segments whereineach of the plurality of transmission segments is transmitted with adifferent beam pattern from a predetermined beamforming codebook;estimate a preferred beamforming vector for the first transceiver fromat least a subset of the plurality of transmission segments and apreferred combining vector for the second transceiver; and send at leastone of the preferred beamforming vector and the preferred combiningvector to the first transceiver during a listening period.
 33. Asubscriber device comprising: one or more antennas; a receiverconfigured to receive, via the antennas, a signal comprising a pluralityof transmission segments wherein each of the plurality of transmissionsegments is transmitted with a different beam pattern from apredetermined beamforming codebook; a processor configured to estimate apreferred beamforming vector from at least a subset of the plurality oftransmission segments and estimate a preferred combining vector; and atransmitter configured to send, via the antennas, at least one of thepreferred beamforming vector and the preferred combining vector during alistening period.